Geoscience Reference
In-Depth Information
c
B
0
∇
·
c
B
0
∇
·
v
e
=
(
E
×
B
0
)=
B
0
·
(
∇
×
E
)
=
iω
b
B
0
=
iω
(
B
0
·
b
)
=
−
iω
∇
·
ξ
⊥
,
B
0
where
b
=(
b
·
B
0
) is a pulsation field component parallel to
B
0
. Hence
z
0
∂N
e
N
e
b
B
0
∂µ
V
3
=
−
iω
dz
(12.33)
0
is proportional to the degree of plasma compression
b
B
0
−
=
∇
·
ξ
⊥
.
V
4
Mechanism
Velo city
V
4
is associated with the change in rates of ion production and loss
when the plasma volume moves by the action of the MHD-wave field. Poole
and Sutcliffe [13] showed that the oscillatory part of
Q
and
L
caused by an
MHD-wave is small and, in the first approximation, it can be set as
V
4
=0
.
Quantitative Treatment
MHD-waves propagating in the meridional plane contain the following non-
zero components (see 7.66):
Alfven wave
b
y
,E
x
,E
y
FMS
b
x
,b
z
,E
y
The Alfven wave electric field lies in the magnetic meridian plane and does not
cause vertical electric drift. If we ignore the longitudinal current transferred
by the Alfven wave, then only the FMS-wave causes vertical electron drift and
plasma compression.
We now find the relation between Doppler velocity and pulsations on the
ground. Let
b
(
i
y
be the amplitude of magnetic field perturbations in the inci-
dent Alfven wave,
b
y
=
b
(
i
y
exp(
ik
A
z
). Equations (7.95), (7.96)
for the reflected FMS-wave in the Cartesian coordinates
−
iωt
+
ikx
−
{
x, y, z
}
(see (7.2))
then gives
R
SA
b
(
i
y
exp(
iI
)exp(
iκ
S
z
)
,
b
(
z
)=
−
(12.34)
k
0
κ
S
R
SA
b
(
i
)
E
y
(
z
)=
−
exp(
iκ
S
z
)
.
(12.35)
y
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